I do apologize that you did not get an answer to your question. Aprelium has provided this forum for users to freely communicate. Not everyone has the time to reply to posts every day. I am glad that you were able to fix the problem on your own. In the future, when you haven't received a reply for a long time, you could always contact Aprelium at support@aprelium.com to see if they can help you with the problem.

The solution to accessing your sites using your domain name locally would be to install a DNS server on your local network and configure your computers to use that as their primary DNS. Alternatively, you could modify the hosts file for every computer that needs to access your server locally. I find the DNS server a much better solution if you have the technical skills to install one. If you choose the hosts file option, modify the hosts file found in %WINDIR%\System32\drivers\etc folder. This is the easier option but requires more work since every computer on the network must be modified for additional host names.

But those do not work, because both of my sites are using the same port (80) in Abyss X2.

In the past, when using different ports, it was easy - I just appended :81 or :82 (etc) to the end of the URL, be it the domain name, or localhost or 127.0.0.1

Internally, all of my PCs are able to access each other without any problem, so modifying their hosts file would not help.

Also, adding entries to the hosts files also would not work in this case, because as Abyss is being run on only 1 PC, these servers are therefore on the same PC, and therefore have the same internal IP ;-)

I just thought there might be a way to access my sites from internally, without having to go out to the Internet, and then back into my network.

I think that your problem may be your router if you are running your server through a wireless network.

Basically your router needs to support loopback which many do not.
No loopback...no can see.
I found out the hard way several years ago when I replaced mine.
I now run a linksys router and access my site internally whenever I want to.